If you don't plan on working on the core C++ packages (but only want to work on / use language pairs), you can install all prerequisites with apt-get, using User:Tino Didriksen's repository. The first line here adds this repository to apt, then we can just install the usual way:

(Note that you have to run that first line, you should not install the apertium-related packages that are in the standard Debian/Ubuntu repos if you want to do development, these are massively out-of-date.)

If you just want to use a language pair, you can also install that with e.g. sudo apt-get install apertium-kaz-tat.

If you want to work on a language pair, you'll have to check out the language data from SVN and compile it (but you can still skip the stuff about installing apertium/lttoolbox/apertium-lex-tools).

Otherwise, e.g. if you want to work on the core C++ packages, install their dependencies with apt-get like this: